Bilateral teleoperation of stochastic port-Hamiltonian systems using energy tanks

In this article we consider the general problem of how to properly endow a stochastic port-Hamiltonian system (SPHS) with an energy tank, that is an energy reservoir that allows to guarantee the passivity property. We show that a stochastic bilateral teleoperation system, composed by a master robot and a slave robot modeled as SPHS, can be connected in a power-preserving manner to energy tanks. The stored energy is continuously monitored to keep the system passive despite time-varying communication delays and interaction with unknown environment that may destabilize the overall system. We will address latter problem considering a SPHS affected by a noise composed by a linear, multiplicative component in Itô form plus an additive one. We underline that such a scenario requires the introduction of an ad hoc notion of passivity.